Two-dimensional Cross-section Research Articles

Fast simulation of 3D elastic response for wheel–rail contact loading using Proper Generalized Decomposition

To increase computational efficiency, we adopt Proper Generalized Decomposition (PGD) to solve a reduced-order problem of the displacement field for a three-dimensional rail head exposed to different contact scenarios. The three-dimensional solid rail head is modeled as a two-dimensional cross-section, with the coordinate along the rail being treated as a parameter in the PGD approximation. A novel feature is that this allows us to solve the full three-dimensional model with a nearly two-dimensional computational effort. Additionally, we incorporate the distributed contact load predicted from dynamic vehicle–track simulations as extra coordinates in the PGD formulation, using a semi-Hertzian contact model. The problem is formulated in two ways; one general ansatz which considers the treatment of numerous parameters, some of which exhibit a linear influence, and a linear ansatz where multiple PGD solutions are solved for. In particular, situations where certain parameters become invariant are handled. We assess the accuracy and efficiency of the proposed strategy through a series of verification examples. It is shown that the PGD solution converges toward the FE solution with reduced computational cost. Furthermore, solving for the PGD approximation based on load parameterization in an offline stage allows expedient handling of the wheel–rail contact problem online.

Designing impact-resistant bio-inspired low-porosity structures using neural networks

Biological structural designs in nature, like hoof walls, horns, and antlers, can be used as inspiration for generating structures with excellent mechanical properties. A common theme in these designs is the small percent porosity in the structure, ranging from 1 to 5%. In this work, the sheep horn was used as an inspiration due to its higher toughness when loaded in the radial direction compared to the longitudinal direction. Under dynamic transverse compression, we investigated the structure-property relations in low porosity structures characterized by their two-dimensional (2D) cross-sections. A diverse design space was created by combining polygonal tubules with different numbers of sides placed on a grid with varying numbers of rows and columns. The volume fraction and the orientation angle of the tubules were also varied. The finite element (FE) method was used with a rate-dependent elastoplastic material model to generate the stress-strain curves under plane-strain conditions. A gated recurrent unit (GRU) model was trained to predict the structures’ stress-strain response and energy absorption under different strain rates and applied strains. The parameter-based model uses eight discrete parameters to characterize the design space and as inputs to the model. The trained GRU model can efficiently predict the response of a new design in as little as 0.16 ms and allows rapid performance evaluation of 128,000 designs in the design space. The GRU predictions identified high-performance structures, and four design trends that affect the specific energy absorption were extracted and discussed.

Characterization and formation mechanism of non-metallic inclusions in single bcc-phase high entropy alloy

This work aims to provide a fundamental study of inclusion characteristics in the single bcc-phase high entropy alloy (HEA), Mn-rich and Al-contained multicomponent system (Al-Cr-Mn-Fe-Co-Ni) was selected as the prototype alloy in this study. According to the differential thermal analysis (DTA) measurements, the solidus (TS) and liquidus (TL) temperatures of this alloy were in the range of 1225–1228 °C (1226 ± 2 °C) and 1268–1271 °C (1270 ± 2 °C), respectively. Non-metallic inclusions were investigated in a two-dimensional (2D) cross-section method as well as extracted by a three-dimensional (3D) electrolytic extraction method. It was found that AlN was the dominant inclusion phase, also a small amount of Al2O3 inclusions were observed. They formed in the liquid alloy and mostly presented as Al2O3-AlN agglomerates, where the size range of the AlN inclusions was larger than that of Al2O3. The theoretical calculation showed that AlN inclusion has a higher coagulation coefficient and collision rate than those of Al2O3 inclusions, which agrees well with the experimental observations. The inclusion characteristics of Al2O3 and AlN were closely related to the relative contents of O and N in the presence of high Al content in the alloy. The impurity elements of N and O were the key issues in controling the stable inclusion phase in high entropic alloy.

(Invited) Designing Transport into Multifunctional Materials for Energy & Power

Designing electrodes and catalytic platforms as architectures in which the entire volume of the porous “reactor” is wired continuously in three dimensions for electron, ion, and molecular transport expands the reactive electrochemical and catalytic turf beyond the limited footprint imposed by a two-dimensional cross-section or a single three-phase boundary per supported nanoparticle. Amplifying the electron/ion/molecularly wired interfacial area by hundreds of square centimeters per cross-sectional square centimeter converts redox reactions that lose morphological control at high local current density into more uniformly reactive events that experience low local current density. Similar distributed arrangement of the reacting species in architected catalytic platforms imparts resilience of the supported catalyst. Aperiodic architectures such as foams and sponges effectively distribute the available reactive, electron/ion/molecularly wired interfaces while maintaining a co-continuous mapping of void and solid to facilitate ingress/egress of reactants and products. Examples from our work with electrode architectures show the power of controlling energy-storage reactions locally by distributing them within electron-wired high-surface interiors. The arrangement ensures that per area current remains low throughout the volume of the electrode, yet the electrified area sums to provide device-relevant current. The intimate interfacial contact we achieve for copper nanoparticles supported on ceria aerogels yields active, selective, and stable architected catalysts for preferential oxidation of carbon monoxide in hydrogen feedstreams.

Identification Of Liquefaction-Potential Zones Using The Gravity Method In Lolu Village, Central Sulawesi

A seismic event of magnitude 7.5 struck the Palu region in Central Sulawesi on September 28, 2018, precipitating a subsequent calamity in the form of a tsunami measuring 4-7 meters in height. This catastrophe was further compounded by the occurrence of liquefaction, leading to extensive devastation and a significant loss of life. In order to identify areas susceptible to liquefaction, it is anticipated that the employment of the gravity method, renowned for its capacity to discern density fluctuations associated with the mass of voluminous materials over a considerable detection range, will prove instrumental. The investigation of parameters and the characterization of liquefaction phenomena in regions previously afflicted by liquefaction disasters can be instrumental in devising strategies for mapping zones that are predisposed to such occurrences. The present study seeks to employ geophysical methods, specifically the gravity method, to delineate zones with the potential for liquefaction within the Lolu Village at Palu City, Central Sulawesi. Through the application of techniques designed to isolate regional and residual anomalies, it is envisaged that a clearer understanding of anomalies situated in shallower regions can be attained, with a specific focus on residential areas. Notably, due to liquefaction, approximately half of the residential areas have shifted a considerable distance of around 132 meters from their original positions. To facilitate the interpretation of subsurface layers, two-dimensional cross-sections are modeled to intersect the displaced and stationary areas. The residual map reveals discernible variations in anomaly values, with lower values observed in the areas that experienced liquefaction-induced movement. Subsurface modeling further demonstrates the presence of three distinct rock layers, namely a sandy layer, a gravel layer, and a rock layer. Additionally, the modeling depicts the formation of canals composed of hard rock, exhibiting varying thicknesses within the surface layer as a consequence of the liquefaction event in 2018. The existence of these canals serves as an indicator that when the sandy layer becomes saturated with water, it will flow along the topographical gradient, following the path of the subterranean canals that have formed.

Hydrodynamics and Wake Flow Analysis of a Floating Twin-Rotor Horizontal Axis Tidal Current Turbine in Roll Motion

The study of hydrodynamic characteristics of floating double-rotor horizontal axis tidal current turbines (FDHATTs) is of great significance for the development of tidal current energy. In this paper, the effect of roll motion on a FDHATT is investigated using the Computational Fluid Dynamics (CFD) method. The analysis was conducted in the CFD software STAR-CCM+ using the Reynolds-averaged Navier–Stokes method. The effects of different roll periods and tip speed ratios on the power coefficient and thrust coefficient of FDHATT were studied, and then the changes in the vorticity field and velocity field of the turbine wake were analyzed by two-dimensional cross-section and Q criterion. The study indicates that roll motion results in a maximum decrease of 30.76% in the average power coefficient and introduces fluctuations in the instantaneous load. Furthermore, roll motion significantly accelerates the recovery of wake velocity. Different combinations of roll periods and tip speed ratios lead to varying degrees of wake velocity recovery. In the optimal combination, at a position 12 times the rotor diameter downstream, roll motion can recover the wake velocity to 92% of the incoming flow velocity. This represents a 23% improvement compared to the case with no roll motion.

Estimating Permeability of Porous Media from 2D Digital Images

Digital rock physics (DRP) has been widely used as an effective approach for estimating the permeability of porous media. However, conventional implementation of DRP requires the reconstruction of three-dimensional (3D) pore networks, which suffer from intensive memory and underlying uncertainties. Therefore, it is highly significant to develop an approach only based on two-dimensional (2D) cross-sections of parent samples without 3D reconstruction. In this study, we present a novel approach that combines the Kozeny–Carman equation with fractal theory to derive a bridge function that links 2D cross-sectional images and 3D pore structures of parent samples in flow equivalence. Using this bridge function, we predicted the physical properties of the parent samples, including the permeability, bulk porosity, tortuosity, and pore fractal dimension. To validate our model, we performed Lattice Boltzmann (LB) simulations on nine carbonate samples and compared the LB simulation results with our model’s predictions. We also compared our predicted results with available data on various porous materials, such as sandstone, glass beads, and carbonate, in the literature. Our findings demonstrate that without reconstructing 3D pore networks, our method provides a reliable estimation of sample permeability using 2D cross-sectional images. This approach not only simplifies the determination of sample permeability in heterogeneous porous media but also sheds new light on the inherent correlations between 2D cross-sectional information and 3D pore structures of parent samples. Moreover, the derived model may be conducible to a better understanding of flow in reservoirs during the extraction of unconventional onshore and offshore oil/gas.

Lift and Drag Analysis of NACA 1412 Airfoil Using Unstructured Mesh

Abstract: This research paper gives insight to the analysis of NACA 1412 airfoil. The airfoil is the two-dimensional cross section of the aircraft’s wing. The aircraft flies due to generation of the lift, this lift is caused by the pressure difference on the upper and lower surface of the airfoil. The pressure on the lower surface is greater than the pressure on upper surface which provides a lift to the airfoil. We are going to see the airfoil’s behaviour in incompressible flow at different angles of attack with constant velocity. In this research, we are going to use the Ansys software to do the analysis. This research is based on the computational fluid dynamics concepts. At the end, we will see how the lift and drag changes at different angles of attack and some graphical results from the research.

Effectiveness of anterior cruciate ligament reconstruction with personalized femoral locator based on apex of deep cartilage

To investigate the effectiveness of anterior cruciate ligament (ACL) reconstruction assisted by personalized femoral locator based on the apex of deep cartilage (ADC) combined with patient imaging data. Between January 2021 and January 2022, a total of 40 patients with primary ACL rupture were selected and randomly divided into study group (ACL reconstruction assisted by personalized femoral locator based on ADC) and control group (ACL reconstruction assisted by intraoperative fluoroscopy and traditional femoral locator), with 20 cases in each group. There was no significant difference in gender, age, body mass index, affected side, cause of injury, and preoperative International Knee Documentation Committee (IKDC) score, Lyshlom score, and Tegner score between the two groups ( P>0.05). IKDC score, Lyshlom score, and Tegner score were used to evaluate the functional recovery of the affected knee before operation and at 3, 6, and 12 months after operation. CT scan and three-dimensional reconstruction were performed before and after operation to measure the horizontal distance from ADC to the anterior cartilage margin (L) and the horizontal distance from ADC to the center of the femoral canal (I), and the anteroposterior position of the bone canal (R) was calculated by I/L; the distance from the center to the distal cartilage margin (D) was measured on the two-dimensional cross section; the R value and D value were compared between the two groups. The operation time of the study group was significantly less than that of the control group [ MD=-6.90 (-8.78, -5.03), P<0.001]. The incisions of the two groups healed by first intention, and no complication such as intra-articular infection, nerve injury, and deep vein thrombosis of lower limbs occurred. There was no significant difference in the R value and D value between the preoperative simulated positioning and the actual intraoperative positioning in the study group [ MD=0.52 (-2.85, 3.88), P=0.758; MD=0.36 (-0.39, 1.11), P=0.351]. There was no significant difference in the actual intraoperative positioning R value and D value between the study group and the control group [ MD=1.01 (-2.57, 4.58), P=0.573; MD=0.24 (-0.34, 0.82), P=0.411]. The patients in both groups were followed up 12-13 months (mean, 12.4 months). The IKDC score, Lysholm score, and Tegner score of the two groups increased gradually with time, and there were significant differences between pre- and post-operation ( P<0.05). There was no significant difference in the scores between the two groups at each time point after operation ( P>0.05). The personalized femoral locator based on ADC can accurately assist the femoral tunnel positioning in ACL reconstruction, which can shorten the operation time when compared with traditional surgical methods, and achieve satisfactory early effectiveness.

Weak form quadrature element analysis of spatial geometrically exact composite beams with torsional warping

Spatial thin-walled laminated composite beams under large deformations with torsional warping effects are studied. A novel two-dimensional cross-section model for composite beams with shear and torsion-warping deformations is proposed wherein the three-dimensional warping and coupling effects caused by inhomogeneous anisotropic materials are considered. A weak form quadrature element formulation is established for nonlinear analysis of geometrically exact composite beams with torsional warping and shear deformations. By combining the two-dimensional cross-section model and the nonlinear one-dimensional beam model, the three-dimensional stress and strain fields can be obtained. Numerical examples are provided to investigate the torsional warping effects and verify the effectiveness of the present formulation. Results of the present beam formulation which are achieved at a significantly lower computational cost are in excellent agreement with those of shell and solid models of commercial codes.

Automatic three-dimensional nasal and pharyngeal airway subregions identification via Vision Transformer

ObjectivesUpper airway assessment requires a fully-automated segmentation system for complete or sub-regional identification. This study aimed to develop a novel Deep Learning (DL) model for accurate segmentation of the upper airway and achieve entire and subregional identification. MethodsFifty cone-beam computed tomography (CBCT) scans, including 24,502 slices, were labelled as the ground truth by one orthodontist and two otorhinolaryngologists. A novel model, a lightweight multitask network based on the Swin Transformer and U-Net, was built for automatic segmentation of the entire upper airway and subregions. Segmentation performance was evaluated using Precision, Recall, Dice similarity coefficient (DSC) and Intersection over union (IoU). The clinical implications of the precision errors were quantitatively analysed, and comparisons between the AI model and Dolphin software were conducted. ResultsOur model achieved good performance with a precision of 85.88–94.25%, recall of 93.74–98.44%, DSC of 90.95–96.29%, IoU of 83.68–92.85% in the overall and subregions of three-dimensional (3D) upper airway, and a precision of 91.22–97.51%, recall of 90.70–97.62%, DSC of 90.92–97.55%, and IoU of 83.41–95.29% in the subregions of two-dimensional (2D) crosssections. Discrepancies in volume and area caused by precision errors did not affect clinical outcomes. Both our AI model and the Dolphin software provided clinically acceptable consistency for pharyngeal airway assessments. ConclusionThe novel DL model not only achieved segmentation of the entire upper airway, including the nasal cavity and subregion identification, but also performed exceptionally well, making it well suited for 3D upper airway assessment from the nasal cavity to the hypopharynx, especially for intricate structures. Clinical significanceThis system provides insights into the aetiology, risk, severity, treatment effect, and prognosis of dentoskeletal deformities and obstructive sleep apnea. It achieves rapid assessment of the entire upper airway and its subregions, making airway management—an integral part of orthodontic treatment, orthognathic surgery, and ENT surgery—easier.

Fractal recognition and contact characteristics of ionic electroactive polymer interface based on microstructure analysis

Interface research is one of the basic topics in the study of mass transfer dynamics and actuation deformation processes. The main objective of this paper is to conduct in-depth research on the interface characteristics of ionic electroactive polymers, and this problem has not been studied to a large extent until now. The formation of the interface is closely related to the factors such as substrate pretreatment, the electroless plating process and the adsorption of ions. The interface has an irregular and self-similar microstructure, fractal theory can well analyze its intrinsic fractal characteristics. Based on the three-dimensional rough interface, the fractal characteristics of six two-dimensional cross-sections were identified. The fractal dimension, relative error, correlation coefficient and scale-free interval obtained by these six methods were quantitatively compared. The interfacial morphological characteristics of the ion-activated polymer were analyzed experimentally and the optimal fractal dimension calculation method was determined. A fractal contact model of the ionic electroactive polymer was developed and the calculation of the peel strength of the interface was proposed. The results show that RMSM is a feasible and effective method for the fractal characterization of the profiles of ionically electroactive polymers. The interfacial contact model based on fractal features can effectively characterize the peeling strength of the interface, which can provide a reference for later microscopic fractal studies on the theories of mass transfer process, actuation deformation and ion migration.

An Application of Mixture Design: A Case Study on Blending of Olive Oils by Design-Expert

or quality control, raw material, semi-finished, and finished product analysis in chemistry, biochemistry, food, and environmental sciences, well-designed experimental strategies are needed to perform all experimental studies at minimum cost and under optimum conditions. The steps in the experimental strategies essentially constitute the experimental procedure followed, and here the aim is to select a model for the experimental procedure, to determine the number of experiments and experimental factor limitations for each run, to identify the correlation between experimental results and factors, and to optimise the experimental factors. The response surface methodology as an experimental design method also reduces the number of experiments required for multi-factor trials for optimisation. Mixture design, a special type of response surface function, is a very effective method for determining the proportions of components or variables in a mixture. A three-component mixture is represented by a triangle, which is a two-dimensional cross-section of a three-dimensional space represented by a cube representing the region where the proportions of the three components are added up to 100%. The points within this triangle or blend area represent possible blends, where: three corners correspond to single components, points along the edges to binary mixtures, the dots in the triangle to triad mixtures, and the centre of the triangle to an equal mix of all three components. Several common designs can be considered as ways to determine the logical number and arrangement of points in a simplex, the most well-known being the Simplex Centroid and Simplex Lattice patterns. This study focused on an experimental design application for fourteen blends of olive oils from four cultivars A–D mixed in the design presented together with a taste panel score for each blend and statistical evaluation of the results for mixture design applications. The higher the score is the better the taste of the olive oil. Here, the mixture design chosen for optimising blending ratios was Simplex-Lattice, and DesignExpert 7.3 software was used for statistical analysis. Comparing of calculated correlation coefficients of the response surface function and its parameters, and function constants, it could be understood that as the correlation coefficient would be 0.21 for used linear terms only, adding quadratic terms into the function increases it to 0.92 drastically.

Dynamics of bubble-shaped Bose–Einstein condensates on two-dimensional cross-section in micro-gravity environment

We investigated the dynamic evolution and interference phenomena of bubble-shaped Bose–Einstein condensates achievable in a micro-gravity environment. Using numerical solutions of the Gross–Pitaevskii equation describing the dynamic evolution of the bubble-shaped Bose–Einstein condensates, we plotted the evolution of the wave function density distribution on its two-dimensional (2D) cross-section and analysed the resulting patterns. We found that changes in the strength of atomic interactions and initial momentum can affect the dynamic evolution of the bubble-shaped Bose–Einstein condensates and their interference fringes. Notably, we have observed that when the initial momentum is sufficiently high, the thickness of the bubble-shaped Bose–Einstein condensate undergoes a counterintuitive thinning, which is a counterintuitive result that requires further investigation. Our findings are poised to advance our comprehension of the physical essence of bubble-shaped Bose–Einstein condensates and to facilitate the development of relevant experiments in micro-gravity environments.

A new computational approach for scoliosis assessment from a non-invasive body scanner

Idiopathic scoliosis is a three-dimensional deformity of the vertebral column and one of the common pediatric spinal diseases, while neuromuscular scoliosis is often associated with cerebral palsy. Especially during periods of growth, there is a high risk of progression of scoliosis. Thus, frequent clinical monitoring is important for proper treatment. X-rays are the Gold standard and the most commonly used method for follow-up of scoliosis. The spinal curvatures are measured by the Cobb angles from x-rays. Patients with scoliosis therefore accumulate higher ionizing radiation doses from repetitive x-rays over their life span. Hence, reducing exposure to ionizing radiation is an important consideration in the follow-up of adolescent scoliosis. For that purpose a body scanner system is proposed, in particular, for complementary diagnostics in children and adolescents with cerebral palsy. The system is non-invasive, free of ionizing radiation and provides three-dimensional scan images of the human torso. In this study, two intermediate steps are described that are useful for the development of analysis methods of the scan images. Two-dimensional transverse cross sections of the torso can be extracted from a scan image along the vertical body axis. Here, methods are described that will be useful for the shape analysis of the two-dimensional transverse body contours. Based on mathematical calculations in polar coordinates, the asymmetry between left and right side of the two-dimensional transverse cross sections is captured by a linear fitting of the course of the contour on either side. Further, the two-dimensional transverse contour data are fitted with an ellipse.

Phase-field study of polycrystalline growth and texture selection during melt pool solidification

Grain growth competition during solidification determines microstructural features, such as dendritic arm spacings, segregation pattern, and grain texture, which have a key impact on the final mechanical properties. During metal additive manufacturing (AM), these features are highly sensitive to manufacturing conditions, such as laser power and scanning speed. The melt pool (MP) geometry is also expected to have a strong influence on microstructure selection. Here, taking advantage of a computationally efficient multi-GPU implementation of a quantitative phase-field model, we use two-dimensional cross-section simulations of a shrinking MP during metal AM, at the scale of the full MP, in order to explore the resulting mechanisms of grain growth competition and texture selection. We explore MPs of different aspect ratios, different initial (substrate) grain densities, and repeat each simulation several times with different random grain distributions and orientations along the fusion line in order to obtain a statistically relevant picture of grain texture selection mechanisms. Our results show a transition from a weak to a strong ⟨10⟩ texture when the aspect ratio of the melt pool deviates from unity. This is attributed to the shape and directions of thermal gradients during solidification, and seems more pronounced in the case of wide melt pools than in the case of a deeper one. The texture transition was not found to notably depend upon the initial grain density along the fusion line from which the melt pool solidifies epitaxially.

Fast stratification of geological cross-section from CPT results with missing data using multitask and modified Bayesian compressive sensing

Since cone penetration test (CPT) is reasonably rapid, affordable, and repeatable, it has been widely used in situ for subsurface soil stratification and classification in geological and geotechnical engineering practice. When used for soil stratification across a 2D geological cross-section, however, it is often observed that some CPTs probe deeper than others, and that some CPT soundings may contain missing data due to presence of gravel-sized particles or intentional bypassing of gravelly soil layers. Arguments above and frequently encountered problem of a small number of CPT soundings in practice pose a great challenge for 2D soil stratification, especially for nonstationary CPT within multilayers. While certain methods have been proposed hoping to address these concerns, they are frequently constrained by either stationary assumption of data, autocorrelation function forms, or computational issues. This study introduces a data-driven multitask Bayesian compressive sensing (MT-BCS) method to estimate missing data for CPT sounding of interest, and then develops a modified 2D BCS method for fast interpolation for horizontal locations without CPT soundings. The proposed method is demonstrated and validated using both numerical and real-world CPT data. Results show that proposed method is both efficient and robust in terms of missing data estimation in each CPT sounding and soil stratification for a 2D geological cross-section.

Effect of basket/rail gap on temperature prediction in the TN-32 cask under storage and drying conditions

This paper investigates the effect of the variation in the gap width between the basket and rails on predicted temperatures in the TN-32 dry storage cask. Two-dimensional (2D) cross-section models of the TN-32 containing thirty-two spent nuclear fuel assemblies generating 30.5 kW of thermal energy are constructed. Storage and vacuum drying pressures, a range of basket/rail gap widths, and shifting of the basket from the cask center, are considered. The simulations include surface-to-surface radiation and gas conduction (including rarefaction), but do not consider natural convection due to the 2D assumption. Results show that the peak cladding temperature, TPC, increases as the gap width increases and as the pressure decreases to vacuum drying (rarefied) levels. As a result, analysis using the nominal unloaded design gap width may overpredict TPC by up to 40 °C under storage conditions and up to 75 °C under vacuum drying conditions. The sensitivity of TPC on pressure is found to decrease as the gap width decreases, and as the basket shifts from the cask center. This paper demonstrates that reducing the uncertainty in the basket/rail gap width by, for example, calculating predictable thermal expansion, and/or statistically quantifying unpredictable manufacturing tolerances and basket shifting, may significantly reduce the uncertainty of peak cladding temperature prediction.

An Automated Mapping Method of 3D Geological Cross-Sections Using 2D Geological Cross-Sections and a DEM

With the three-dimensional (3D) geological information system development, 3D geological cross-sections (GCs) have become the primary data for geological work and scientific research. Throughout past geological surveys or research works, a lot of two-dimensional (2D) geological cross-section maps have been accumulated, which struggle to meet the scientific research and application needs of 3D visual expression, 3D geological analysis, and many other aspects. Therefore, this paper proposes an automatic generation method for 3D GCs by increasing the dimensions based on a digital elevation model (DEM) and 2D geological cross-section maps. By matching corresponding nodes, generating topographic feature lines, constructing an affine transformation matrix, and inferring the elevation value of each geometric node on the GC, the 3D transformation of the 2D GCs is realized. In this study, fourteen 2D GCs within Nanjing City, Jiangsu Province, are transformed into 3D GCs using the proposed method. The transformed results and quantitative error show that: (1) the proposed method applies to both straight and bent GCs; (2) each transformed GC can fit seamlessly with the ground and maintain minimal geometric deformation, and the geometric shape is consistent with the original GC in non-mountains area. This paper corroborated the proposed method’s effectiveness by comparing it with the other two 3D transformation strategies. In addition, the transformed GCs can be subjected to 3D geological modeling and digital Earth presentation, achieving positive effects in both 3D application and representation.

Reconstructing Three-dimensional geological structures by the Multiple-point statistics method coupled with a deep neural network: A case study of a metro station in Guangzhou, China

A credible large-scale three-dimensional (3D) geological model constructed from a small amount of local high-density data provides a vital data infrastructure for the design and construction of metro lines. The multiple-point statistics (MPS) method has successfully generated 3D geological models in many fields. However, the global cognition of the spatial relations between geological objects is difficult to reconstruct using a local optimization strategy with moving templates in the MPS simulation. This study presented an MPS simulation approach for constructing 3D geological structures with two-dimensional (2D) cross-sections, where the MPS process was coupled with a fully connected deep neural network (FCDNN) simulation. The core idea of the proposed method was that the global features of each geological object were generated from the trained FCDNN, the input parameter of which was the subsurface depth. Then, the entire model was constructed on the initial model using the following iterative MPS process: the semantic relationship of geological objects was extracted from 2D cross-sections and used as a constraint in the modeling process, which ensured the order of the stratigraphic sequence and rationality of the geological structure in the final model. The joint objective function of the proposed method was composed of the loss function of the FCDNN and conventional MPS objective function constrained by the spatial semantics of geological objects. The concrete example in the Jiangtai Road Metro Station of Guangzhou Line 11, China illustrated that the details of the complex geological structures could be obtained accurately by the presented method. The global features from the trained FCDNN provided the basic geometry for the final model, which overcame the limitations of the conventional MPS method.